Time Dilation Calculator

Time Dilation Explained

Einstein's theory of relativity predicts that time doesn't pass at the same rate for everyone — it slows down for objects moving at high speed, and separately, slows down in stronger gravitational fields.

Special relativity (velocity): $$t' = \frac{t}{\sqrt{1 - v^2/c^2}}$$

General relativity (gravity): $$t' = \frac{t}{\sqrt{1 - \frac{2GM}{rc^2}}}$$

The factor 1/√(1−v²/c²) is called the Lorentz factor, often written γ (gamma).

Worked Example: A Fast-Moving Spacecraft

Using the velocity mode's defaults — an observer moving at 0.1c for a proper time of 3600 seconds (one hour) — the Lorentz factor is $\gamma = 1/\sqrt{1-0.01} \approx 1.005$, so a stationary observer would measure about 3618 seconds elapsing, roughly 18 seconds more. At everyday speeds this effect is utterly negligible, but it grows dramatically as velocity approaches the speed of light — at 0.99c, the same hour would stretch to over 7 hours from the stationary observer's perspective.

Why GPS Satellites Need Both Corrections

GPS satellites orbit fast enough that special relativity slows their onboard clocks by about 7 microseconds per day relative to Earth's surface, but they also sit high enough that Earth's weaker gravity at that altitude speeds their clocks up by about 45 microseconds per day — a general relativistic effect that runs in the opposite direction. The net result is that GPS clocks run about 38 microseconds per day faster than clocks on the ground, and engineers must build that correction directly into the satellite systems, or GPS positioning would drift by kilometers within a day.

A Brief History of Time Dilation

Albert Einstein introduced velocity-based time dilation in his 1905 special relativity paper, building on earlier mathematical work by Hendrik Lorentz that gave the effect its name. Gravitational time dilation followed in his 1915 general theory of relativity, which reframed gravity itself as the curvature of spacetime. Both predictions have since been confirmed to extraordinary precision — modern atomic clocks are sensitive enough to detect gravitational time dilation from a height difference of just a single meter.

Common Time Dilation Mistakes

Assuming time dilation is symmetric in a way that lets both observers consistently claim the other's clock is slower without resolution is a common conceptual trap — this only becomes a genuine paradox (the "twin paradox") when acceleration or gravity breaks the symmetry, which relativity fully accounts for. Confusing which observer's time is the "proper time" (the shorter one, measured by the moving or lower-altitude clock) versus the "dilated time" (the longer one) is another frequent mix-up. Assuming the effect only matters for spacecraft or exotic scenarios, when it's a routine part of engineering systems like GPS, is a third common oversight.

Relativity Terms You Should Know

Proper Time — the time measured by a clock in its own reference frame, always the shortest possible measurement.

Lorentz Factor (γ) — the multiplier by which time, length, and mass are affected at a given velocity.

Spacetime Curvature — general relativity's description of gravity as a warping of space and time itself.

Twin Paradox — a classic thought experiment illustrating time dilation between a traveling and a stationary twin.

The gravitational mode assumes a non-rotating spherical mass and a static observer; it does not account for the observer's own motion, which would require combining both effects.